Matematychni Studii最新文献_第8页

On some properties of Hassani transforms 关于Hassani变换的一些性质

Matematychni Studii Pub Date : 2022-03-31 DOI: 10.30970/ms.57.1.79-91

Y. Grushka

引用次数: 1

The least dimonoid congruences on relatively free trioids 相对自由三似体上最小二似体同余

Matematychni Studii Pub Date : 2022-03-31 DOI: 10.30970/ms.57.1.23-31

A. Zhuchok

{"title":"The least dimonoid congruences on relatively free trioids","authors":"A. Zhuchok","doi":"10.30970/ms.57.1.23-31","DOIUrl":"https://doi.org/10.30970/ms.57.1.23-31","url":null,"abstract":"When Loday and Ronco studied ternary planar trees, they introduced types of algebras,called trioids and trialgebras. A trioid is a nonempty set equipped with three binary associativeoperations satisfying additional eight axioms relating these operations, while a trialgebra is justa linear analog of a trioid. If all operations of a trioid (trialgebra) coincide, we obtain the notionof a semigroup (associative algebra), and if two concrete operations of a trioid (trialgebra)coincide, we obtain the notion of a dimonoid (dialgebra) and so, trioids (trialgebras) are ageneralization of semigroups (associative algebras) and dimonoids (dialgebras). Trioids andtrialgebras have close relationships with the Hopf algebras, the Leibniz 3-algebras, the Rota-Baxter operators, and the post-Jordan algebras. Originally, these structures arose in algebraictopology. One of the most useful concepts in algebra is the free object. Every variety containsfree algebras and free objects in any variety of algebras are important in the study of thatvariety. Loday and Ronco constructed the free trioid of rank 1 and the free trialgebra. Recently,the free trioid of an arbitrary rank, the free commutative trioid, the free n-nilpotent trioid, thefree rectangular triband, the free left n-trinilpotent trioid and the free abelian trioid wereconstructed and the least dimonoid congruences as well as the least semigroup congruence onthe first four free algebras were characterized. However, just mentioned congruences on freeleft (right) n-trinilpotent trioids and free abelian trioids were not considered. In this paper, wecharacterize the least dimonoid congruences and the least semigroup congruence on free left(right) n-trinilpotent trioids and free abelian trioids.","PeriodicalId":37555,"journal":{"name":"Matematychni Studii","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-03-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42084488","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

$mathscr{T}$-Commuting Generalized Derivations on Ideals and Semi-Prime Ideal-II $mathscr｛T｝$-理想和半素理想II上的交换广义导子

Matematychni Studii Pub Date : 2022-03-31 DOI: 10.30970/ms.57.1.98-110

N. Rehman, Hafedh M. Alnoghashi

引用次数: 1

Stable range conditions for abelian and duo rings 阿贝尔环和二重环的稳定值域条件

Matematychni Studii Pub Date : 2022-03-31 DOI: 10.30970/ms.57.1.92-97

A. Dmytruk, A. Gatalevych, M. Kuchma

引用次数: 1

On certain subclass of Dirichlet series absolutely convergent in half-plane 在半平面上绝对收敛的狄利克雷级数的某一子类

Matematychni Studii Pub Date : 2022-03-31 DOI: 10.30970/ms.57.1.32-44

M. Sheremeta

{"title":"On certain subclass of Dirichlet series absolutely convergent in half-plane","authors":"M. Sheremeta","doi":"10.30970/ms.57.1.32-44","DOIUrl":"https://doi.org/10.30970/ms.57.1.32-44","url":null,"abstract":"Denote by $mathfrak{D}_0$ a class of absolutely convergent in half-plane $Pi_0={scolon text{Re},s<0}$ Dirichlet series$F(s)=e^{sh}-sum_{k=1}^{infty}f_kexp{s(lambda_k+h)},, s=sigma+it$, where $h> 0$, $h<lambda_kuparrow+infty$ and $f_k>0$.For $0lealpha<h$ and $lge 0$ we say that $F$ belongs to the class $mathfrak{DF}_h(l,alpha)$ if and only if$text{Re}{e^{-hs}((1-l)F(s)+frac{l}{h}F'(s))}>frac{alpha}{h}$,and belongs to the class $mathfrak{DG}_h(l,alpha)$ if and only if$text{Re}{e^{-hs}((1-l)F'(s)+frac{l}{h}F''(s))}>alpha$ for all $sin Pi_0$. It is provedthat $Fin mathfrak{DF}_h(l,alpha)$ if and only if $ sum_{k=1}^{infty}(h+llambda_k)f_kle h-alpha$, and$Fin mathfrak{DG}_h(l,alpha)$ if and only if $sum_{k=1}^{infty}(h+llambda_k)(lambda_k+h)f_kle h(h-alpha)$. \u0000If $F_jin mathfrak{DF}_h(l_j,alpha_j)$, $j=1, 2$, where $l_jge0$ and $0le alpha_j<h$, then Hadamard composition$(F_1*F_2)in mathfrak{D}F_h(l,alpha)$, where $l=min{l_1,l_2}$ and$alpha=h-frac{(h-alpha_1)(h-alpha_2)}{h+llambda_1}$. Similar statement is correct for the class $F_jin mathfrak{DG}_h(l,alpha)$. \u0000For $j>0$ and $delta>0$ the neighborhood of the function $Fin mathfrak{D}_0$ is defined as follows$O_{j,delta}(F)={G(s)=e^{s}-sum_{k=1}^{infty}g_kexp{slambda_k}in mathfrak{D}_0colon sum_{k=1}^{infty}lambda^j_k|g_k-f_k|ledelta}$. It is described the neighborhoods of functions from classes $mathfrak{DF}_h(l,alpha)$ and $mathfrak{DG}_h(l,alpha)$. \u0000Conditions on real parameters $gamma_0,,gamma_1,,gamma_2,,a_1$ and $a_2$ of the differential equation $w''+(gamma_0e^{2hs}+gamma_1e^{hs}+gamma_2) w=a_1e^{hs}+a_2e^{2hs}$ are found, under which this equation has a solutioneither in $mathfrak{DF}_h(l,alpha)$ or in $mathfrak{DG}_h(l,alpha)$.","PeriodicalId":37555,"journal":{"name":"Matematychni Studii","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-03-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42605731","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 1

Boundary value matrix problems and Drazin invertible operators 边值矩阵问题与Drazin可逆算子

Matematychni Studii Pub Date : 2022-03-31 DOI: 10.30970/ms.57.1.16-22

K. Miloud Hocine

引用次数: 0

Universally prestarlike functions associated with shell like domain 类壳结构域的普遍类星前函数

Matematychni Studii Pub Date : 2022-03-31 DOI: 10.30970/ms.57.1.53-61

K. Vijaya, G. Murugusundaramoorthy, S. Yalçın

引用次数: 0

Well-posedness of the Cauchy problem for system of oscillators on 2D–lattice in weighted $l^2$-spaces 加权$ 1 ^2$-空间中二维格上振子系统Cauchy问题的适定性

Matematychni Studii Pub Date : 2021-12-27 DOI: 10.30970/ms.56.2.176-184

S. Bak, G. Kovtonyuk

{"title":"Well-posedness of the Cauchy problem for system of oscillators on 2D–lattice in weighted $l^2$-spaces","authors":"S. Bak, G. Kovtonyuk","doi":"10.30970/ms.56.2.176-184","DOIUrl":"https://doi.org/10.30970/ms.56.2.176-184","url":null,"abstract":"We consider an infinite system of ordinary differential equations that describes the dynamics of an infinite system of \u0000linearly coupled nonlinear oscillators on a two dimensional integer-valued lattice. It is assumed that each oscillator \u0000interacts linearly with its four nearest neighbors and the oscillators are at the rest at infinity. We study the initial value problem (the Cauchy problem) for such system. This system naturally can be considered as an operator-differential equation \u0000in the Hilbert, or even Banach, spaces of sequences. We note that $l^2$ is the simplest choice of such spaces. With this choice of the configuration space, the phase space is $l^2times l^2$, and the equation can be written in the Hamiltonian form with the Hamiltonian $H$. Recall that from a physical point of view the Hamiltonian represents the full energy of the system, i.e., the sum of kinetic and potential energy. Note that the Hamiltonian $H$ is a conserved quantity, i.e., for any solution of equation the Hamiltonian is constant. For this space, there are some results on the global solvability of the corresponding Cauchy problem. In the present paper, results on the $l^2$-well-posedness are extended to weighted $l^2$-spaces $l^2_Theta$. We suppose that the weight $Theta$ satisfies some regularity assumption. \u0000Under some assumptions for nonlinearity and coefficients of the equation, we prove that every solution of the Cauchy problem from $C^2left((-T, T); l^2)$ belongs to $C^2left((-T, T); l^2_Thetaright)$. \u0000And we obtain the results on existence of a unique global solutions of the Cauchy problem for system of oscillators on a two-dimensional lattice in a wide class of weighted $l^2$-spaces. These results can be applied to discrete sine-Gordon type equations and discrete Klein-Gordon type equations on a two-dimensional lattice. In particular, the Cauchy problems for these equations are globally well-posed in every weighted $l^2$-space with a regular weight.","PeriodicalId":37555,"journal":{"name":"Matematychni Studii","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2021-12-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43175815","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

A counterexample to Henry E. Dudeney’s star puzzle Henry E. Dudeney的星星谜题的反例

Matematychni Studii Pub Date : 2021-12-27 DOI: 10.30970/ms.56.2.215-217

A. Ravsky

引用次数: 0

Interpolation rational integral fraction of the Hermitian-type on a continual set of nodes 连续节点集上埃尔米特型的插值有理积分分数

Matematychni Studii Pub Date : 2021-12-27 DOI: 10.30970/ms.56.2.185-192

Y. Baranetskij, I. Demkiv, M. Kopach, A. Solomko

{"title":"Interpolation rational integral fraction of the Hermitian-type on a continual set of nodes","authors":"Y. Baranetskij, I. Demkiv, M. Kopach, A. Solomko","doi":"10.30970/ms.56.2.185-192","DOIUrl":"https://doi.org/10.30970/ms.56.2.185-192","url":null,"abstract":"Some approaches to the construction of interpolation rational integral approximations with arbitrary multiplicity of nodes are analyzed. An integral rational Hermitian-type interpolant of the third order on a continual set of nodes, which is the ratio of a functional polynomial of the first degree to a functional polynomial of the second degree, is constructed and investigated. The resulting interpolant is one that holds any rational functional of the resulting form. \u0000Проаналізовано ряд підходів до побудови інтерполяційних раціональних інтегральних наближень з довільною кратністю вузлів. Будується та досліджується інтегральний раціональний інтерполянт типу Ерміта третього порядку на континуальній множині вузлів, який є відношенням функціонального полінома першого степеня до функціонального полінома другого степеня. Одержаний інтерполянт є таким, що зберігає будь який раціональний функціонал одержаного вигляду.","PeriodicalId":37555,"journal":{"name":"Matematychni Studii","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2021-12-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47435794","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0